Problem: 6 people can paint 4 walls in 43 minutes. How many minutes will it take for 7 people to paint 7 walls? Round to the nearest minute.
We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 4\text{ walls}\\ p &= 6\text{ people}\\ t &= 43\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{4}{43 \cdot 6} = \dfrac{2}{129}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 7 walls with 7 people. $t = \dfrac{w}{r \cdot p} = \dfrac{7}{\dfrac{2}{129} \cdot 7} = \dfrac{7}{\dfrac{14}{129}} = \dfrac{129}{2}\text{ minutes}$ $= 64 \dfrac{1}{2}\text{ minutes}$ Round to the nearest minute: $t = 65\text{ minutes}$